Unlike ferromagnets, antiferromagnets typically exhibit fully compensated magnetic moments and thus nearly zero net magnetization, posing challenges to the design and manipulation of antiferromagnetic spintronic devices. Recent studies have demonstrated that antiferromagnets can host spin-orbit coupling (SOC)-induced spontaneous Zeeman-type spin splittings (ZSSs), while electric fields and strain can also induce such spin splittings, giving rise to spin-polarized carriers in these materials and therefore opening new avenues for antiferromagnetic spintronics. In this review, we systematically discuss the physical mechanisms underlying ZSSs in antiferromagnetic materials, with particular emphasis on the linear magnetoelectric, linear piezomagnetic, and bilinear piezomagnetoelectric effects that induce ZSSs via electric fields, strain, and electric field-strain coupling, respectively. We also construct the corresponding effective Hamiltonians for spontaneous and the aforementioned field-induced ZSSs. Within both nonrelativistic and relativistic frameworks, we classify the spin point groups (SPGs) and magnetic point groups (MPGs) that allow for spontaneous and externally induced ZSSs. By comparing the symmetry constraints imposed by SPGs and MPGs, we can elucidate the SOC dependence of the corresponding ZSSs in antiferromagnets. This review aims to provide a theoretical basis for screening antiferromagnetic materials with tunable ZSSs and designing antiferromagnetic spintronic devices.